UPSC Prelims 2015 · CSAT
Question 74: Basic Numeracy
In a society it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 handshakes. Which one among the following numbers indicates the possible number of hugs ?
AnswerUPSC’s answer is (c).
Handshakes happen only between a man and a woman who are friends, hugs between friends of the same sex. Taking m men and w women who are all friends, handshakes = m × w = 24 and hugs = mC2 + wC2. Test the splits of 24: 4 and 6 give 6 + 15 = 21 hugs; 3 and 8 give 3 + 28 = 31; 2 and 12 give 1 + 66 = 67; 1 and 24 give 276. Only 21 is among the options.
Why each option is right or wrong
- (a) Wrong: no split of 24 handshakes gives 39 hugs.
- (b) Wrong: no split gives 30 hugs.
- (c) Right: 4 men and 6 women, or the reverse, give 6 + 15 = 21 hugs.
- (d) Wrong: no split gives 20 hugs.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2015, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.